This is pretty silly about Peter's dagger and his speaking to John.
The last supper accounts clearly tell of Peter signaling (and whispering?) to John during the supper. Also John tells of how Peter with a sword cut off the High Priest's servant's ear, during Jesus' arrest, in the Garden of Gethsemene the same evening as the supper. Luke says Jesus told them to get swords (for self defense), then (in Matthew) after Peter's violence, tells him to put it up (with the famous phrase "those who live by the sword die by the sword...")...and then (Luke tells us) Jesus heal's the servant's ear. Showing Peter with sword (or dagger) at the supper is not menacing to John, rather hinting of what he'd do later.
There are lots of details in the gospel accounts which DaVinci clearly was aware of. Also Renaissance Humanism was starting to portray religious figures as more naturally human....hence no halos--DaVinci was cutting edge, of course, so what--but Albegensian? Ha!
The only reason such theories gain traction is through biblical ignorance.
Also Judas Thadeous has no link to Judas Iscariot, the traitor. For DaVinci to paint himself in is not at all unusual...(Rembrandt did it too, along with various other masters) very clever, yes....cutting edge, yes...OK then, meet Leonardo.
And having a knot symbolizing his family sign in the painting? What does that have to do with the Cathari?
You're right, of course. You already mentioned a couple of the obvious points: the dagger or little "sword" has to do with Peter cutting off the ear of Malchus in the garden; Jude (Judas Thaddeus) is a different disciple from Judas Iscariot ("Jude" or "Judas" was a very common name, since Judah was one of Israel's patriarchs).